In a large measuring cup, whisk together milk, butter, egg, and vanilla.
In the bowl of a standing mixer fitted with a dough hook, add 3 cups flour, sugar, yeast, salt, and cinnamon. With the mixer on low speed, add the milk mixture and mix until the dough comes together, about 2 minutes.
Add raisins and increase mixer speed to medium and mix until the dough is smooth and elastic, 9 to 10 minutes. After 5 minutes, the dough should clear the sides of the bowl (have pulled away) but stay attached at the bottom. If the dough is sticking to the sides of the bowl, add the remaining flour, 1 tablespoon at a time, until the dough clears the side of the bowl.
Turn the dough out on to a clean surface and shape into a ball. Coat a large bowl with nonstick spray. Place the dough in the bowl, turning once to cover evenly in nonstick spray, then cover tightly with plastic wrap. Place in a warm, draft-free area to rise until doubled in volume, about 2 hours. See notes for help creating a place for the dough to rise.
Coat a 9-inch x 13-inch baking dish with nonstick spray or line with parchment paper. Turn the risen dough out on to a lightly floured surface and divide into 12 equal pieces. Shape each piece into a tightly formed bun and place in the prepared baking dish, seam side down.
Cover the buns with plastic wrap coated with nonstick spray. Place in a warm, draft-free area to rise until doubled in volume and touching, about 1 hour. See notes for help creating a place for the dough to rise.
Preheat oven 375ºF. To make the egg wash, whisk together egg and water. Brush gently over the buns. Bake until the buns are deep golden brown and the interiors have reached 190ºF, about 20 to 25 minutes. Cool completely, ate least 30 minutes.
To make the glaze, whisk together powdered sugar, milk, and vanilla in a small bowl. Using a spoon, drizzle the glaze in an cross pattern on top of each bun. I found it easiest to do a long, continuous line in one direction across the buns in a row, and then repeat in a perpendicular direction for each row.